ION IMPLANTATION DISTRIBUTION GENERATION METHOD AND SIMULATOR
An ion implantation distribution generation method for causing a computer to generate an ion implantation distribution, the method causing the computer to perform: generating distributions related to Rp lines each representing a range projection Rp in a surface subjected to ion implantation in a device structure of a semiconductor integrated circuit; drawing the Rp lines on a two-dimensional diagram corresponding to an ion implantation condition; and generating, for each of the Rp lines, a two-dimensional impurity concentration distribution in accordance with two-dimensional vector coordinates provided to the Rp line.
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This application is based upon and claims the benefit of priority from the prior Japanese Patent Application NO. 2010-073364 filed on Mar. 26, 2010, the entire contents of which are incorporated herein by reference.
FIELDThe embodiments discussed herein are related to an ion implantation distribution generation method and a simulator.
BACKGROUNDIn the development of state-of-the-art MOSFETs (Metal Oxide Semiconductor Field Effect Transistors) for LSI (Large-Scale Integration), accurate prediction, by simulation, of an ion implantation distribution in a MOS structure has become considerably important in recent years in terms of evaluation of electrical characteristics.
For example, there have been proposed a method of performing accuracy fitting between the theoretical value of the standard deviation of variations in the depth direction caused by changes in ion incident angle and the experimental value obtained by SIMS (Secondary Ion Mass Spectroscopy) with the use of the standard deviation of variations in the transverse direction as a fitting parameter, to thereby empirically identity the standard deviation in the transverse direction, and a method of simulating the ion implantation distribution in the MOS structure with the use of a simple analysis model using such a standard deviation in the transverse direction (see Japanese Laid-open Patent Publication No. 2000-138178 and Suzuki K., Tanabe R., and Kojima S., “Analytical Model for Two-Dimensional Ion Implantation Profile in MOS-Structure Substrate,” IEEE Trans. Electron Devices, Vol. ED-56, No. 12, pages 3083 to 3089, 2009, for example).
Other related art includes: Hisamoto D., Lee W.-C., Kedzierski J., Takeuc hi H., Asano K., Kuo C., Anderson E., King T.-J., Bokor J., and Hu C., “FinFET-A Self-Aligned Double-Gate MOSFET Scalable to 20 nm,” IEEE Trans. Electron Devices, Vol. ED-47, No. 12, pages 2320 to 2325, 2000; Ryu S.-W., Han J.-W., Kim C.-J., and Choi Y.-K., “Investigation of Isolation-Dielectric Effects of PDSOI FinFET on Capacitorless 1T-DRAM,” IEEE Trans. Electron Devices, Vol. ED-56, No. 12, pages 3232 to 3235, 2009; Wada T. and Kotani N., “Design and Development of 3-Dimensional Process Simulator,” IEICE. Trans. Electron, Vol. E82-C, No. 6, pages 839 to 847, 1999; and Ohkura Y., Suzuki C., Mise N., Matsuki T., Eimori T., and Nakamura M., “Monte Carlo Investigation of Potential Fluctuation in 3D Device Structure,” Semiconductor Leading Edge Technologies, [online], Sep. 9, 2008 (retrieved from <http://www.selete.co.jp/?lang=EN&act=Research&sel_no=103> on The Internet on Feb. 24, 2010).
The above-described related art is advantageous in that the introduction of an analysis model into the simulation of a two-dimensional ion implantation distribution allows a reduction in calculation time, as compared with the simulation based on numerical calculation, and that the physical image of the MOS structure is easily grasped. In terms of the model to be incorporated into a device simulator, however, the related art has an issue in that, if the obtained shape deviates from a similar figure, a new model needs to be derived and incorporated into the simulator every time the deviation occurs.
For example, in a transistor device having a three-dimensional structure, such as FinFET (Fin Field Effect Transistor) which has attracted attention in recent years, the analysis model and the numerical calculation are complicated, and it is not easy to perform simulation of a three-dimensional ion implantation distribution.
SUMMARYAccording to one aspect of the embodiments, there is an ion implantation distribution generation method for causing a computer to generate an ion implantation distribution. The method is configured to cause the computer to perform, the method including: generating distributions related to Rp lines each representing a range projection Rp in a surface subjected to ion implantation in a device structure of a semiconductor integrated circuit, drawing the Rp lines on a two-dimensional diagram corresponding to an ion implantation condition, and agenerating, for each of the Rp lines, a two-dimensional impurity concentration distribution in accordance with two-dimensional vector coordinates provided to the Rp line.
The object and advantages of the embodiments will be realized and attained by means of the elements and combinations particularly pointed out in the claims.
It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory and are not restrictive of the embodiments, as claimed.
Embodiments of the present invention will be described below on the basis of the drawings. Description will be first made of the impurity concentration distribution in each of the steps of an ion implantation process.
Assumption:
(First Step) Substrate: The impurity concentration distribution is represented by the following formula (1) on the assumption that the concentration is constant.
N1(x,y)=Nsub N0(x,y)=Nsub (1)
(Second Step) Channel Ion Implantation Distribution: The channel ion implantation is performed on the entire surface of the substrate not formed with a gate electrode. The impurity concentration distribution is, therefore, represented by the following formula (2).
(Third Step) Extension Region Ion Implantation Distribution: The impurity concentration distribution is represented by the following formula (3) on the assumption that a gate electrode having a length LG has been formed.
(Fourth Step) Source and Drain Region Ion Implantation Distribution: Further, the impurity concentration distribution is represented by the following formula (4) on the assumption that a side wall having a thickness Lside has been formed on both sides of the gate electrode.
Herein, φ, Rp, ΔRp, and ΔRpt in each of the formulae respectively represent the dose, the range projection, the straggling of the range projection in a longitudinal direction, and the straggling of the range projection in a transverse direction in each ion implantation condition.
Further, a fifth step corresponds to the pocket ion implantation process. The pocket ion implantation process includes the steps illustrated in
In general, the pocket ion implantation is performed in four directions, as illustrated in the drawings, to maintain symmetry. The pocket ion implantation is performed while the substrate is rotated around the center of the surface thereof as an axis, and the four directions are determined by, for example, rotation angles of 0°, 90°, 180°, and 270°. That is, as illustrated in
In this case, the analysis is separately performed on a region a1 in which the concentration is determined independently of the presence or absence of the gate electrode 4, and a region a2 in which the concentration is affected by the side wall of the gate electrode 4. The regions a1 and a2 are represented as ion implantation regions divided by a straight line perpendicular to the tilt angle α and passing through a connection point A of the side wall of the gate electrode 4 and the surface of the substrate 1.
On the left side of the gate electrode 4, there are a region blocked by the gate electrode 4 and thus not subjected to the ion implantation and a region b subjected to the ion implantation (hereinafter referred to as the region b subjected to shadowing by the gate electrode 4). The region b is represented as an ion implantation region extending in a direction away from the gate electrode 4 from an intersection point B at which the surface of the substrate 1 intersects with a straight line extending at the tilt angle α from a top portion of a side wall of the gate electrode 4. Strictly speaking, some components of ion beams 9 pass through the top portion of the gate electrode 4 and reach the substrate 1. In the following, however, such components will be ignored, and the gate electrode 4 will be assumed to completely block the ion beams 9 in the above-described region.
Then, as illustrated in
Further,
The region a1 will be first examined with reference to
For graphical clarification, the origin D is herein set to a position far from an end of the gate electrode 4, as illustrated in
In the formula (5), erf( ) represents an error function. Herein, the following equation holds.
σ12=ΔRp2 cos2α+ΔRpt2 sin2 α (6)
Herein, variable transformation is performed by reference to
Thereby, the following equations are derived.
The above-described formula (5) is, therefore, represented by the following formula (8), which uses a function including only y, as described above.
Subsequently, the region a2 will be examined with reference to
Herein, the origin is set to an end A of the gate. By reference to
The first term of the formula (9) is affected by the side wall of the gate electrode 4, while the second term of the formula (9) is unaffected by the gate electrode 4.
The formula (9) is similarly subjected to the variable transformation, and is represented by the following formula (10).
Herein, the following equation holds.
σ22=ΔRp2 sin2α+ΔRpt2 cos2 α (11)
Then, evaluation is performed on the formula (10) on the border y=x·tan α between the regions a1 and a2. The second term of the formula (10) represents the contribution by the gate pattern region. Thus, only the first term may be taken into account. If y=x·tan α is substituted into the first term of the formula (10) to eliminate x, the following formula (12) is derived.
The difference between the formula (12) and the foregoing formula (8) is in the numerator. If the numerator of the formula (12) is calculated, therefore, the calculation result matches the numerator of the formula (8), as illustrated in the following formula (13).
Herein, if the origin is shifted from the end of the gate to the center of the gate with a change from x to x−LG/2 in the formula (10), the following formula (14) is obtained.
The border between the regions a1 and a2 is represented by the following formula (15).
Herein, if approximation is performed as ΔRp≈ΔRpt, the following simplified formula (16) is derived.
Subsequently, the region b subjected to the shadowing by the gate electrode 4 will be examined with reference to
Also in this case, the formula is subjected to integration and thereafter variable transformation. Thereby, the following formula (18) is derived.
The distance between the origin B and the center of the gate is represented as dG·tan α+LG/2. If the origin B is shifted to the center of the gate, therefore, the following formula (19) is derived.
With the use of the above-described formulae, a method for further simplification will be described below. The two-dimensional model based on the formulae presented in “Assumption” described above will be referred to as the “analysis model,” and a simplified two-dimensional model obtained by simplification of the “analysis model” will be referred to as the “simplified analysis model.”
In “Assumption,” Rp, ΔRp, and ΔRpt represent the range projection, the straggling of the range projection in the longitudinal direction, and the straggling of the range projection in the transverse direction, respectively. On the basis of the above-described formulae (6) and (11), therefore, a collision cross section σ1 in the longitudinal direction and a collision cross section σ2 in the transverse direction obtained by the interaction between the implanted ions and the nuclei of the substrate 1 may be respectively represented as follows.
σ1=√{square root over (ΔRp2 cos2 α+ΔRpt2 sin2 α)} (20)
σ1=√{square root over (ΔRp2 sin2 α+ΔRpt2 cos2 α)} (21)
The above formulae are subjected to approximation to be simplified.
The approximation is first performed as ΔRp≈ΔRpt, and the following equation is set.
ΔRp=ΔRpt=σ1=σ2≡σ (22)
Accordingly, the formula (14) is represented as follows.
If x is a large value, therefore, the following equation holds.
The formula (24) is compared with the formula (8) for the region a1. The coefficient in front of the formula (8) indicates that the surface side has no contribution to the concentration.
When the depth from the surface reaches or exceeds √2σ tan α, approximation is performed as follows.
If the collision cross section σ in the formula (24) is replaced by σ1, the formulae match each other. In view of this, the following equation is proposed which uses σ1 and σ2 as the collision cross section σ in the longitudinal direction and the collision cross section σ in the transverse direction, respectively, in the formula (23).
This configuration is expected to provide an effect of compensating for the degradation of accuracy caused by the rough approximation ΔRp≈ΔRpt used so far. The formula (26) matches the approximate formula (25) for the region a1 in the limit of a large x value. That is, the formula (26) is used as an effective approximate formula for the regions a1 and a2.
The approximation of the formula (24) is also used for the region b, and the following equation is derived.
Also in this case, when the depth reaches or exceeds √2σ tan α, simplification is performed as follows.
Also in the formula (28), the collision cross section σ in the longitudinal direction and the collision cross section σ in the transverse direction are replaced by σ1 and σ2, respectively. Thereby, the following equation is derived.
The pocket ion implantation concentration distribution N4
N4
The distribution obtained by the third ion implantation with the rotation angle of 0° and the distribution obtained by the fourth ion implantation with the rotation angle of 180° are both represented as follows.
The pocket ion implantation distribution is represented by the following equation which sums the above values.
Therefore, the sum of the respective values of the above-described formulae (1), (2), (3), (4), and (32) corresponds to the total impurity concentration distribution in the entire ion implantation process.
The drawing further illustrates two-dimensional ion implantation distributions in a MOS-structure substrate having a gate length of 0.2 μm subjected to the pocket ion implantation, wherein the doping has been performed under an ion implantation condition of ions of B, acceleration energy of 10 keV, a dose of 9×1012 cm−2, and a tilt angle of 27°. In this case, Rp, ΔRp, and ΔRpt are 38.41 nm, 30.9 nm, and 16.0 nm, respectively, and it is understood that the simplified analysis model 7a and the analysis model 7b substantially match each other.
In
In
The simplified analysis model 7a and the analysis model 7b match each other well both in the two-dimensional impurity concentration distribution in the longitudinal direction at an end of the gate, which is illustrated in
The simplified analysis model 7a well reproduces the analysis model 7b and the result of the numerical calculation.
To verify, under wider conditions, the accuracy of the simplified analysis model 7a in this case, the result of examination to find whether or not an equation ΔRpt=rΔRp is consistent with the distributions is illustrated in
In a second embodiment, description will be made of a method of geometrically interpreting the simplified analysis model to apply the simplified analysis model to a generalized analysis model independent of the MOS structure, and allowing the simplified analysis model to be expanded into a three-dimensional model.
With the use of the following formula (34) in the simplified formula (26) for the region a, coordinate transformation into the Rp line is performed.
Thereby, the following equation is derived which is represented in a simpler form.
The coordinate transformation into the Rp line corresponds to the transformation into rectilinear coordinates representing the range projection Rp (peak concentration position). The straight line represented by the transformed coordinates will be referred to as the “Rp line” in the present embodiment.
In a similar manner, coordinate transformation into the Rp line is performed by the use of the following formula (36) in the simplified formula (29) for the region b.
Thereby, the following equation is derived.
With the formulae (35) and (37), the two-dimensional distribution in a patterned substrate of any shape may be easily geometrically interpreted and generated as follows. In the ion implantation into a given pattern, straight lines each representing the range projection Rp are first drawn. The respective straight lines may correspond one-to-one to the surfaces subjected to the ion implantation.
The two-dimensional impurity concentration distribution related to one Rp line is represented in the following form in any case.
Herein, v and u respectively represent a unit vector in a vertical direction and a unit vector in a horizontal direction with respect to a plane, and the direction from an implanted region to an unimplanted region corresponds to the positive direction. Further, θ represents an angle relative to the vertical direction with respect to the plane.
As illustrated in
Accordingly, the two-dimensional impurity concentration distribution is defined is a generalized Rp line as illustrated in
If the semi-infinite straight line is easier to handle in the analysis, the formula (38) is used as reqeted.
Subsequently, description will be made of the expansion into the three-dimensional model with reference to examples of the rotation angles of 0°, 90°, 180°, and 270°. In the ion implantation into the surface 13f in
When the Rp lines 14a, 14b, 14c, and 14d are represented as a gs
The three-dimensional impurity concentration distribution in this case is represented as follows.
The above three-dimensional model is limited to the rotation angles of 0°, 90°, 180°, and 270°.
Further, a general polygon may be drawn on the xy-plane. The tilt angle may be set to an arbitrary value, but limited in the plane and not in the z-direction, i.e., the tilt angle of an arbitrary value may be set in a quasi-three-dimensional structure.
In the case of a rectangular shape, the application in the z-direction is also possible, as illustrated in an application example described below.
Application Example to Three-Dimensional StructureDescription will be made of an example in which the above-described three-dimensional analysis model is applied to FinFET (see Hisamoto D. et al. and Ryu S.-W. et al. included in the above-mentioned related art), which has attracted attention as an advanced device.
An example is now assumed wherein the ion implantation is performed at the tile angle α with the rotation angles of 90° and 270° to dope the source region 58a and the drain region 58b. The impurity concentration distribution NR90 for the rotation angle of 90° will be first discussed.
An Rp line 1 represents a straight line drawn in the source region 58a on the basis of the range projection Rp from the upper surface of the region, and an Rp line 2 represents a straight line drawn in the source region 58a on the basis of the range projection Rp from a side surface of the region subjected to the ion implantation. Further, an Rp line 3 represents a straight line drawn in the substrate 51 on the basis of the range projection Rp from a surface of the substrate subjected to the ion implantation. A distance D represents the length from the right side surface of the substrate 51 subjected to the ion implantation to the Rp line 2.
The origin is set at the center of each of the Rp lines 1, 2, and 3, and the formula (37) is applied with coordinates (u1, v1), (u2, v2), and (u3, v3) each representing the vertical and horizontal directions with respect to the corresponding surface. The Rp lines represented as gs all correspond to the pattern c illustrated in
With the application of the formula (37), the two-dimensional impurity concentration distribution related to the Rp line 1 is represented as follows.
NR90
The variable transformation is represented as follows.
With the application of the formula (37), the two-dimensional impurity concentration distribution related to the Rp line 2 is represented as follows.
NR90
The variable transformation in this case is represented as follows.
The two-dimensional impurity concentration distribution related to the Rp line 3 does not contribute to the channel region, but will be described herein for the sake of generality.
NR90
The variable transformation in this case is represented as follows.
In any case, the following equations hold.
Therefore, the two-dimensional impurity concentration distribution NR90 for the rotation angle of 90° is obtained by the sum of the two-dimensional impurity concentration distributions NR0
NR90=NR90
The two-dimensional impurity concentration distribution for the rotation angle of 270° is symmetrical with the above-described distribution with respect to the yz-plane with an x value of 0, and thus is represented as follows.
NR
Subsequently, an example of the rotation angle of 0° will be discussed. Description of specific calculations will be omitted. In this case, the Rp lines as illustrated in
An Rp line 1 represents a straight line drawn in the source region 58a on the basis of the range projection Rp from the upper surface of the region. Further, an Rp line 2 represents a straight line drawn in the gate electrode 54 on the basis of the range projection Rp from a side surface of the electrode subjected to the ion implantation, and an Rp line 3 represents a straight line drawn in the gate electrode 54 on the basis of the range projection Rp from the upper surface of the electrode. Further, an Rp line 4 represents a straight line drawn in the drain region 58b on the basis of the range projection Rp from a portion of the upper surface of the region subjected to the ion implantation (a portion not blocked by the gate electrode 54).
A height dG represents the height from the upper surface of the drain region 58b to the upper surface of the gate electrode 54, and a distance G represents the distance from the center of the gate electrode 54 to a side surface of the substrate 51.
The origin is set at the center of each of the Rp lines 1, 2, 3, and 4, and the formula (37) is applied with coordinates (u1, v1), (u2, v2), (u3, v3), and (u4, v4) each representing the vertical and horizontal directions with respect to the corresponding surface. As for the horizontal direction s in this case, the definition of the Rp line is directly used. The Rp line having the width W in the horizontal direction s (x-direction) corresponds to the Rp line 14b of
With the application of the formula (37), the two-dimensional impurity concentration distribution related to the Rp line 1 is represented as follows.
The variable transformation in this case is represented as follows.
With the application of the formula (37), the two-dimensional impurity concentration distribution related to the Rp line 2 is represented as follows.
NR
The variable transformation in this case is represented as follows.
With the application of the formula (37), the two-dimensional impurity concentration distribution related to the Rp line 3 is represented as follows.
NR0
The variable transformation in this case is represented as follows.
With the application of the formula (37), the two-dimensional impurity concentration distribution related to the Rp line 4 is represented as follows.
The variable transformation in this case is represented as follows.
In any of the above cases, the following equations hold.
According to the above description, the two-dimensional impurity concentration distribution NR0 for the rotation angle of 0° is obtained by the sum of the two-dimensional impurity concentration distributions NR0
NR0(x,y,z)=NR0
The two-dimensional impurity concentration distribution for the rotation angle of 180° is symmetrical with the above-described distribution with respect to the xy-plane with a z value of 0, and thus is represented as follows.
NR
Accordingly, the three-dimensional impurity concentration distribution in the FinFET 50 is obtained on the basis of the respective two-dimensional impurity concentration distributions for the rotation angles of 0°, 90°, 180°, and 270°.
It is now assumed that the doping is performed with the structure parameters of the FinFET 50 set as a width W of 50 nm, a height H of 200 nm, and a gate length LG of 0.1 μm, and with the ion implantation condition set as ions of As, acceleration energy of 30 keV, a dose of 1×1015 cm−2, a tilt angle of 30°, and rotation angles of 90° and 270°. In this case, Rp, ΔRp, and ΔRpt are 25.9 nm, 11.2 nm, and 11.0 nm, respectively.
Each of
In the longitudinal one-dimensional cut concentration distribution illustrated in
The transverse one-dimensional cut concentration distribution illustrated in
Subsequently, description will be made of simulation results of the two-dimensional impurity concentration distribution on the cross sections in the z-direction, i.e., on the zy-plane and the zx-plane.
As illustrated in
The one-dimensional cut concentration distribution illustrated in
Description will be made of a simulator configuration for realizing, irrespective of the above-described shape of the semiconductor device, the two-dimensional impurity concentration distribution and three-dimensional impurity concentration distribution resulting from the ion implantation.
The CPU 11 controls the simulator 100 in accordance with a program stored in the memory unit 12. A RAM (Random Access Memory), a ROM (Read-Only Memory), and the like are used for the memory unit 12, which stores, for example, programs executed by the CPU 11, data requested for the processing by the CPU 11, and data obtained through the processing by the CPU 11. Further, a part of the area of the memory unit 12 is allocated as a work area for use in the processing by the CPU 11.
The display unit 13 displays a variety of requested information under the control of the CPU 11. The output unit 14, which includes a printer and so forth, is used to output a variety of information in accordance with an instruction from a user. The input unit 15, which includes a mouse, a keyboard, and so forth, is used to allow the user to input a variety of information requested for the processing of the simulator 100. The communication unit 16 is a device connected to, for example, the Internet, a LAN (Local Area Network), or the like to control communication with an external device. The storage device 17, which uses a hard disk unit, for example, stores data such as a program for performing a variety of processes.
A program realizing the processing performed by the simulator 100 is provided to the simulator 100 by a storage medium 19, such as a CD-ROM (Compact Disc Read-Only Memory), for example. That is, as the storage medium 19 storing the program is set in the driver 18, the driver 18 reads the program from the storage medium 19, and the read program is installed in the storage device 17 via the system bus B. Then, upon start of the program, the CPU 11 starts the processing thereof in accordance with the program installed in the storage device 17. The medium storing the program is not limited to the CD-ROM, and may be any computer-readable medium.
The program realizing the processing according to the first and second embodiments may also be downloaded by the communication unit 16 through a network and installed in the storage device 17. Further, if the simulator 100 supports USB (Universal Serial Bus), the program may be installed from a USB-connectable external storage device. Further, if the simulator 100 supports flash memory, such as an SD (Secure Digital) card, the program may be installed from such a memory card.
The distribution parameter generation unit 32 is a processing unit which generates, in accordance with the input of an ion implantation condition 31 and with the use of an experimental database 41, the range projection Rp of the ion implantation, the straggling ΔRp of the range projection in the depth direction, the straggling ΔRpt of the range projection in the transverse direction, and high-order moments γ and β. The ion implantation condition 31 specifies the implantation ion, the substrate type, the implantation energy, the dose, the tile angle, and so forth. The experimental database 41 stores a table which includes distribution parameters according to the implantation energy associated with respective combinations of the implantation ion and the substrate type.
The simplified analysis model creation unit 33 includes a simplification processing unit 33e, an Rp line creation unit 33f, and a pattern selection unit 33g. The simplification processing unit 33e is a processing unit which realizes a simplified analysis model capable of illustrating the pocket ion implantation distribution in the region b and the region a combining the regions a1 and a2 illustrated in
The simplified analysis model creation unit 33 further includes a calculation processing unit for calculating the impurity concentration distribution resulting from the ion implantation into each of the substrate, the channel region, the extension region, and the source and drain regions. The drawing, however, only illustrates the processing units concerning the present embodiment of the pocket ion implantation distribution, and omits the illustration of other components.
The two-dimensional concentration distribution generation unit 34 is a processing unit which performs numerical calculation to calculate, for each of the ion beams 9 and in accordance with the mesh size on the xy-plane, the ion implantation concentration in the substrate applied with the ion beams 9, to thereby generate a two-dimensional concentration distribution resulting from the ion implantation.
The device simulation unit 35 is a processing unit which evaluates an electrical characteristic by generating the corresponding distribution parameter from the ion implantation condition 31.
The three-dimensional concentration distribution generation unit 37 is a processing unit which performs numerical calculation to calculate, for each of the ion beams 9 and in accordance with the mesh size on the xyz-plane, the ion implantation concentration in the substrate applied with the ion beams 9, to thereby generate a three-dimensional concentration distribution resulting from the ion implantation.
The two-dimensional concentration distribution generation unit 34 and the three-dimensional concentration distribution generation unit 37 receive from the simplified analysis model creation unit 33 the Rp lines each representing the shape and the peak concentration position of the impurity concentration distribution in each of the steps of the ion implantation process, and thus may be integrated into one processing unit.
The distribution parameter generation unit 32, the simplified analysis model creation unit 33, the two-dimensional concentration distribution generation unit 34, and the device simulation unit 35 operate as a two-dimensional process device simulator which verifies an electrical characteristic on the basis of the two-dimensional concentration distribution, and also operate as a two-dimensional inverse modeling simulator which verifies the two-dimensional concentration distribution on the basis of a desired electrical characteristic and optimizes the two-dimensional concentration distribution.
Further, the distribution parameter generation unit 32, the simplified analysis model creation unit 33, the three-dimensional concentration distribution generation unit 37, and the device simulation unit 35 operate as a three-dimensional process device simulator which verifies an electrical characteristic on the basis of the three-dimensional concentration distribution, and also operate as a three-dimensional inverse modeling simulator which verifies the three-dimensional concentration distribution on the basis of a desired electrical characteristic and optimizes the three-dimensional concentration distribution.
Subsequently, with reference to
In
Then, the simplification processing unit 33e sets the value σ to obtain a correct formula in the limit, to thereby compensate for the approximation of ΔRp≈ΔRpt (Step S12). At Step S12, the value σ in the longitudinal direction and the value σ in the transverse direction are replaced by σ1 and σ2, respectively, in the respective impurity concentration distribution formulae (23) and (28) for the regions a and b. Thereby, the formulae (26) and (29) are derived.
Then, to generate the two-dimensional concentration distribution resulting from the ion implantation, Steps S13 to S16 and Step S20 are performed. Meanwhile, to generate the three-dimensional concentration distribution resulting from the ion implantation, Steps S17 to S20 are performed.
The Rp line creation unit 33f generates the distributions related to the Rp lines (Step S13). If the Rp lines are approximated with semi-infinite straight lines, the Rp line creation unit 33f generates the two-dimensional impurity concentration distributions corresponding thereto (Step S14). The impurity concentration distribution formula (39) is applied at Step S13, and the impurity concentration distribution formula (38) is applied at Step S14.
To generate the two-dimensional concentration distribution, the Rp line creation unit 33f draws the Rp lines on a two-dimensional diagram corresponding to the ion implantation condition (Step S15). For example, the Rp lines 12-1, 12-2, and 12-3 as illustrated in
As for the pocket ion implantation distribution, the two-dimensional concentration distribution generation unit 34 generates, in accordance with the Rp lines drawn on the two-dimensional diagram and with the use of the impurity concentration distribution formula (39) or (38) to be applied, the two-dimensional concentration distribution by performing numerical calculation, and also generates the two-dimensional concentration distribution for each of the other steps of the ion implantation process (Step S16).
In the simulation of the two-dimensional concentration distribution, Steps S17 to S19 are omitted, and the electrical characteristic evaluation by the device simulation unit 35 is performed with the use of the result of the two-dimensional concentration distribution (Step S20).
Further, to generate the three-dimensional concentration distribution, the pattern selection unit 33g of the simplified analysis model creation unit 33 selects the pattern of the Rp line in the horizontal direction s on the basis of the shape of the device, and applies the function according to the selected pattern (Step S17). That is, the pattern selection unit 33g selects, for each of the angles for ion implantation, one pattern according to the shape of the device from the patterns a to d illustrated in
Then, to generate the three-dimensional concentration distribution, the Rp line creation unit 33f draws the Rp lines on a three-dimensional diagram corresponding to the ion implantation condition (Step S18). For example, the Rp lines 1 to 3 as illustrated in
As for the pocket ion implantation distribution, in accordance with the Rp lines drawn on the three-dimensional diagram and with the use of the impurity concentration distribution formula to be applied, the three-dimensional concentration distribution generation unit 37 generates, for each of the rotation angles, the three-dimensional concentration distribution by performing numerical calculation, and also generates the three-dimensional concentration distribution for each of the other steps of the ion implantation process (Step S19). As for the pocket ion implantation distribution, the formulae (50), (51), (61), and (62) are applied for the rotation angles of 90°, 270°, 0°, and 180°, respectively.
Then, with the use of the result of the three-dimensional concentration distribution, the electric characteristic evaluation by the device simulation unit 35 is performed (Step S20).
The above-described embodiments allows the first introduction of a simplified analysis model of the pocket ion implantation distribution. Further, it is possible to realize substantially the same accuracy as the accuracy obtained by numerical calculation, and to obtain a physical image. Further, the embodiments are capable of flexibly following the device structure, and automatically generating the two- and three-dimensional impurity concentration distributions according to the device structure.
The present embodiments are not limited to the specifically disclosed embodiments, and may be modified or altered in various ways without departing from the scope of the claims.
All examples and conditional language recited herein are intended for pedagogical purposes to aid the reader in understanding the invention and the concepts contributed by the inventor to furthering the art, and are to be construed as being without limitation to such specifically recited examples and conditions, nor does the organization of such examples in the specification relate to a depicting of the superiority and inferiority of the invention. Although the embodiments of the present invention have been described in detail, it should be understood that the various changes, substitutions, and alterations could be made hereto without departing from the spirit and scope of the invention.
Claims
1. An ion implantation distribution generation method for causing a computer to generate an ion implantation distribution, the method causing the computer to perform:
- generating distributions related to Rp lines each representing a range projection Rp in a surface subjected to ion implantation in a device structure of a semiconductor integrated circuit;
- drawing the Rp lines on a two-dimensional diagram corresponding to an ion implantation condition; and
- generating, for each of the Rp lines, a two-dimensional impurity concentration distribution in accordance with two-dimensional vector coordinates provided to the Rp line.
2. The ion implantation distribution generation method according to claim 1, wherein the two-dimensional impurity concentration distribution is generated by using of formula (63) N ( u, v ) = 1 2 erfc ( u 2 σ u ) × Φ cos θ 2 π σ v exp [ - v 2 2 σ v 2 ] ( 63 )
- wherein v and u respectively represent a unit vector in a vertical direction and a unit vector in a horizontal direction with respect to a plane, and the direction from an implanted region to an unimplanted region corresponds to a positive direction, and
- wherein θ represents an angle relative to a vertical direction with respect to the plane.
3. The ion implantation distribution generation method according to claim 2, the method causing the computer to further perform:
- selecting, on basis of the presence or absence of contribution of the ion implantation in the device structure, the pattern of the Rp line in another horizontal direction s different from the horizontal direction u in a three-dimensional diagram;
- drawing the Rp lines on the three-dimensional diagram corresponding to the ion implantation condition; and
- generating, for each of the Rp lines, a three-dimensional impurity concentration distribution by using the formula (63) in accordance with two-dimensional vector coordinates provided to the Rp line.
4. The ion implantation distribution generation method according to claim 3, wherein in the drawing the Rp lines on the three-dimensional diagram corresponding to the ion implantation condition, a function according to the pattern selected in selecting the pattern of the Rp line in another horizontal direction s different from the horizontal direction u in a three-dimensional diagram is used.
5. The ion implantation distribution generation method according to claim 1, the method causing the computer to further perform:
- when generating an ion implantation distribution at a high tilt angle, simplifying a shape of the impurity concentration distribution in each of ion implantation distribution regions, which have different influences on a channel region in accordance with the gate structure, by approximating variations in a longitudinal direction and variations in a transverse direction; and
- compensating for the approximation of the variations in the longitudinal direction and the variations in a transverse direction so as to obtain a correct shape in the limit in an unshadowed region of the ion implantation distribution regions.
6. The ion implantation distribution generation method according to claim 5, the method causing the computer to further perform:
- performing device simulation for evaluating an electrical characteristic of the device structure of the semiconductor integrated circuit on the basis of the two-dimensional impurity concentration distribution or the three-dimensional impurity concentration distribution.
7. The ion implantation distribution generation method according to claim 4, the method causing the computer to further perform:
- performing inverse modeling for generating the two-dimensional impurity concentration distribution or the three-dimensional impurity concentration distribution corresponding to a desired electrical characteristic.
8. The ion implantation distribution generation method according to claim 1, wherein the semiconductor integrated circuit is a metal oxide semiconductor field effect transistor or a fin field effect transistor.
9. A computer-readable storage medium for storing a computer-executable program for causing a computer to function as a simulator which generates an ion implantation distribution, the program causing the computer to perform:
- generating distributions related to Rp lines each representing a range projection Rp in a surface subjected to ion implantation in a device structure of a semiconductor integrated circuit;
- drawing the Rp lines on a two-dimensional diagram corresponding to an ion implantation condition; and
- generating, for each of the Rp lines, a two-dimensional impurity concentration distribution in accordance with two-dimensional vector coordinates provided to the Rp line.
10. A process device simulator for evaluating an electrical characteristic by using an ion implantation distribution, the simulator comprising:
- means for generating distributions related to Rp lines each representing a range projection Rp in a surface subjected to ion implantation in a device structure of a semiconductor integrated circuit;
- means for drawing the Rp lines on a two-dimensional diagram or a three-dimensional diagram corresponding to an ion implantation condition;
- means for generating, for each of the Rp lines, a two-dimensional impurity concentration distribution or a three-dimensional impurity concentration distribution in accordance with two-dimensional vector coordinates provided to the Rp line; and
- means for performing device simulation for evaluating the electrical characteristic of the device structure of the semiconductor integrated circuit on the basis of the two-dimensional impurity concentration distribution or the three-dimensional impurity concentration distribution.
11. The process device simulator according to claim 10, wherein the process device simulator is configured to optimize the impurity concentration distribution corresponding to a desired electrical characteristic.
Type: Application
Filed: Mar 21, 2011
Publication Date: Sep 29, 2011
Applicant: FUJITSU LIMITED (Kawasaki-shi)
Inventor: Kunihiro Suzuki (Kawasaki)
Application Number: 13/052,612
International Classification: G06F 17/10 (20060101);